Children's gestures can reveal important information about their problem-solving strategies. This study investigated whether the information children express only in gesture is accessible to adults not trained in gesture coding. Twenty teachers and 20 undergraduates viewed videotaped vignettes of 12 children explaining their solutions to equations. Six children expressed the same strategy in speech and gesture, and 6 expressed different strategies. After each vignette, adults described the child's reasoning. For children who expressed different strategies in speech and gesture, both teachers and undergraduates frequently described strategies that children had not expressed in speech. These additional strategies could often be traced to the children's gestures. Sensitivity to gesture was comparable for teachers and undergraduates. Thus, even without training, adults glean information, not only from children's words but also from their hands. How does a skilled teacher identify when a child experiences a "teachable moment" and decide what type of instruction to offer that child? For instruction to be beneficial, it must be timed appropriately visa -vis the child's developing knowledge. Further, to be maximally effective, the type of instruction must mesh appropriately with the knowledge the child brings to the learning situation (Kuhn, 1972; Turiel, 1969). However, despite the importance of the match between the child and the learning environment (Hunt, 1961), little is known about the sources of information that teachers use, both to gauge when a particular child is ready to learn and to decide what type of instructional input to offer that child. The notion of readiness to learn is present in many theories of developmental change. For example, in the Piagetian view, the "teachable moment" is one characterized by disequilibrium, or instability of knowledge. During periods of disequilibrium, children are hypothesized to be especially receptive to input from the environment that helps them

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This paper discusses the benefits and limitations of using children's literature in introducing science concepts to young children. The manuscript also provides an overview of preschool science standards of 12 states and presents lists of appropriate children's literature suitable to use in teaching science concepts targeted in those preschool science standards.

Not all relevant instructional information comes in the form of spoken words. In the present study, the authors examine multiple modalities of nonspoken forms of representation-specifically gestures, pictures, objects, and writing-used by 3 teachers in 3 years of lst-grade math lessons. Teachers frequently used visually based modalities of representation and tended to produce combinations of representational forms rather than isolated representations. There were individual differences in their preference for representation types. Teachers used representations to accompany important spoken terms and to respond to student confusion. With nonspoken representations, teachers conveyed information critical to the explanation of mathematical concepts. Students must attend to the visual as well as vocal means of expressing information to gain access to all of the information presented in mathematics lessons.

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In the past 25 years an identifiable interest in using children’s literature in mathematics learning emerged (Clyne and Griffiths, 1991; Welchman-Tischler, 1992; Hong, 1996; Hellwig etal., 2000; Haury, 2001). We critically review the rationales given for the use of picture books in mathematics learning, with a special focus on geometry due to its underrepresentation in this body of literature and the need for greater focus on this topic. The benefits and effectiveness of using picture books for children’s mathematics learning and interest have been documented (Hong, 1996; O’Neill etal., 2004; Young-Loveridge, 2004). For geometry, although much learning of shape ideas should be hands-on, two-dimensional figures are essential to develop children’s understanding of plane geometry. Books may effectively engage pre-literate children with plane shapes (van den Heuvel-Panhuizen and van den Boogaard, 2008; Skoumpourdi and Mpakopoulou, 2011) and shapes as gestalt wholes or prototypes (van Hiele, 1986; Clements etal., 1999; Hannibal, 1999). We review several guidelines and evaluative criteria for book selection, including Cianciolo (2000), Schiro (1997), Hunsader (2004), and van den Heuvel-Panhuizen and Elia (2012). Geometry concepts have proven challenging for young students, but their difficulties may stem, in part, from inadequate teacher training and professional development (Clements and Sarama, 2000; Chard etal., 2008) which lead to misconceptions (Oberdorf and Taylor-Cox, 1999; Inan and Dogan-Temur, 2010). Using picture books in teacher training may be an inviting way for early childhood teachers to enhance their own knowledge. We will examine the literature for guidance on incorporating children’s literature into teacher training. In closing we will outline a comprehensive, multi-pronged agenda for best instructional practices for selection and use of children’s books in mathematics activities and for teacher training.

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